Decimals/Transcript
Transcript Text reads: The Mysteries of Life with Tim and Moby Tim and Moby are at a swim meet. Tim is timing a race. As the first swimmer finishes, his stopwatch reads 39.83 seconds. TIM: Nice! 39 and eighty-three hundredths! A letter appears. Tim reads from the typed letter. TIM: Dear Tim and Moby, can you make a movie about decimals? From, Veronica. Sure can! Basically, a decimal is a number that's based on the number 10. Actually, all of our numbers are decimals, because our number system is based on 10. Even the word, decimal, comes from the Latin word for 10 -- decem. But usually, when people talk about decimals, they're talking about numbers that are only parts of a whole. MOBY: Beep? TIM: Imagine you've got a rectangle that represents one whole object. An image shows a rectangle. TIM: If you divide it into 10 smaller, equal-sized rectangles, you now have 10 parts of one -- tenths! Lines appear and divide the rectangle into 10 smaller rectangles. TIM: If you divide each of those into 10 smaller rectangles, you have 10 times 10, or 100 parts of one -- hundredths! Lines appear and divide the 10 rectangles into 100 rectangles. TIM: Now, if you divide each of those into 10 smaller rectangles, you have 10 times 100, or 1,000 parts of one -- thousandths! More lines appear and divide the 100 rectangles into 1000 rectangles. TIM: All of these fractions: tenths, hundredths, and thousandths; are called, decimal units. MOBY: Beep. TIM: Well, writing decimals is pretty easy. In our number system, I can count from 0 to 9, in the units place. An animation shows a digital stopwatch, with empty slots for 5 digits. Each slot is labeled with its place value. The leftmost slot is labeled, tens; the second slot from the left is labeled, units; the middle slot is unlabeled; the second slot from the right is labeled, tenths; the rightmost slot is labeled, hundredths. A red arrow points to the slot labeled "units," as the number 9 appears in the units slot. TIM: To count bigger numbers, I have to move left, over to the tens place. The red arrow moves to the tens slot, and the number 3 appears in the tens slot, to the left of the 9. As a result, the number displayed changes from 9 to 39. TIM: Each place increases by a power of 10. Because decimal units are smaller than 1 unit, you actually move to the right of the units place. To do that, you need this guy -- the decimal point. The red arrow moves to the unlabeled third slot where a decimal point appears, to the right of 39. TIM: Numbers to the left of the decimal point are whole numbers, and numbers to the right are decimals. The number 8 appears in the slot labeled tenths, located to the right of the decimal point. The number 3 appears in the slot labeled hundredths, to the right of the tenths slot. The stopwatch now reads, 39.83. TIM: Except for the units, every place on the left side has a decimal equivalent on the right. Tens and tenths. The red arrow splits into two red arrows, which point move to the tens and tenths places. TIM: Hundreds and hundredths. A new slot appears to the left of the tens place, labeled, hundreds. The red arrows move to the hundreds and hundredths places. TIM: Thousands and thousandths. A new slot appears to the left of the hundreds place, labeled thousands. A new slot appears to the right of the hundredths place, labeled thousandths. The red arrows move to the thousands and thousandths places. TIM: So this number is 39, and 83 hundredths. Moby shrugs. MOBY: Beep! TIM: Actually, decimals are really important. We use them every day to talk about money. An image shows two price tags. One reads 29.99, or, 29 dollars and 99 cents. The other reads 3.19, or 3 dollars and 19 cents. MOBY: Beep. TIM: Right, one cent is just one-hundredth of a dollar. An animation shows the price tags being buried beneath a pile of pennies. TIM: We can also use decimals for weight, measuring distances, baseball statistics, temperatures, and even stock prices. A split screen shows images of a scale, a ruler, a batting average, a thermometer, and a stock ticker. MOBY: Beep? TIM: You need more reasons? Well, arithmetic is a lot easier with decimals than it is with fractions. As long as you line the decimal points up, you can add or subtract them just like whole numbers. An image shows an addition problem reading 19.40 plus 3.02 equals 22.42. TIM: Also, decimal numbers are easy to compare. An animation shows two decimals side by side: 4.05, and 4.0092. The first decimal, 4.05, moves to the row above the second decimal, 4.0092. Two zeros are added to the end of 4.05, so that it has four digits after the decimal point, just like 4.0092. TIM: By adding zeros to the right of the shorter number to make the numbers the same length, you can tell right away which one is bigger. Two zeros are added to the right of number 4.05. It now reads 4.0500. A greater than symbol appears, showing that this number is bigger than 4.0092. MOBY: Beep? TIM: Well, zero is just a placeholder. Adding zeroes to the right of a decimal number doesn’t change the value of the number. MOBY: Beep? TIM: Some decimals do go on adding numbers to the right forever. For example, the decimal equivalent of the fraction one-third starts out as 0.3333 and just keeps going on, and on, and on. An image shows the fraction one-third. Behind it, an animation shows the numbers 0.333. More threes are added to the right until they fill the screen. TIM: These decimals are called repeating decimals. A label appears, reading, repeating decimals. TIM: You could round that number off to three-tenths or 33 hundredths, but it’s more accurate to put a line over the last number. That line indicates that the number keeps on going. The screen now shows that the fraction one-third equals 0.33, with a line over the last 3. TIM: Decimals that end are called terminating decimals. An image shows the decimal 4.95. TIM: But some decimals, called irrational numbers, don't end or repeat. One example is pi, which is the ratio of the circumference of a circle to its diameter. An image shows a circle with a line drawn through its center. TIM: Pi starts off 3.14159; and then it keeps going and going, without any repeating pattern. The decimal, 3.14159 appears above the red circle. An animation shows more digits of pi being added to the end until they fill the screen. TIM: Convinced yet? MOBY: Beep. Moby shrugs. The crowd cheers as another race comes to a finish. Tim clicks the stopwatch. Cassie emerges from the water, just before Rita emerges. The stopwatch reads, 39.82 seconds which is the same than 39.83 seconds. TIM: One-hundredth of a second faster than Rita! Cassie lifts her arm in triumph. TIM: See? Decimals matter! Category:BrainPOP Transcripts